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GAZA CITY, Gaza Strip — Palestinian militants hit an Israeli city with a rocket from Gaza for the first time yesterday, causing no casualties but drawing a pledge of harsh retaliation from Israel, which was already in the midst of a military offensive.

Prime Minister Ehud Olmert called the rocket fire on the coastal city of Ashkelon a “major escalation,” coming just hours after a deadline set by the militants holding an Israeli soldier passed with Israel rejecting demands to release about 1,500 Palestinian prisoners. The militants said they would not harm 19-year-old Cpl. Gilad Shalit — if he is still alive. But they warned that they would provide no further information about him.

Early today, Israeli aircraft struck the Palestinian Interior Ministry in Gaza for the second time in a week, the military said. Witnesses said missiles hit the main structure again and damaged a building next to the ministry, which has been used since the first attack. Rescue workers said five persons were wounded.

In other attacks early today, Israeli aircraft fired missiles at a Hamas camp in southern Gaza and a Hamas-affiliated school in Gaza City.

The Palestinian rocket flew seven miles through the air and exploded in the courtyard of a school in Ashkelon, a city of 110,000 on Israel’s coast north of Gaza. The school was empty at the time, and no one was hurt. School security cameras showed a large cloud of white dust rising from the point of impact.

Although militants have fired many of the small, homemade rockets in the direction of Ashkelon, this was the first one to hit the heart of the city, displaying a longer range than most previous ones and bringing the threat of rocket barrages to a major Israeli population center for the first time.

“For this attempt that was meant to harm Israeli civilians who live in the sovereign borders of Israel, there will be far-reaching consequences,” Mr. Olmert warned at a U.S. Independence Day celebration at the home of Richard Jones, the U.S. ambassador to Israel. “The Hamas organization will be the first to feel this.”

Israel launched the Gaza offensive, punctuated by nightly air strikes, to put pressure on Cpl. Shalit’s kidnappers — Hamas-affiliated militants who seized the soldier in a June 25 cross-border raid. But the militants responded with defiant demands for the release about 1,500 prisoners from Israeli jails.

On Monday, the Hamas-affiliated militants set a 6 a.m. yesterday deadline for Israel to begin complying and implied that they would kill Cpl. Shalit if it refused. But the deadline passed without event, and a spokesman for the Army of Islam, one of the three groups that kidnapped Cpl. Shalit, said the militants “decided to freeze all contacts and close the case on this soldier.”

“We will not give any information that will give the occupation good news or reassurance,” said the spokesman, Abu Muthana, who added, “We will not kill the soldier, if he is still alive.”

Hours after the deadline passed, Mr. Olmert was defiant.

“We won’t negotiate with terror elements, and we won’t let anyone believe that kidnapping is a tool to bring Israel to its knees,” he said.

Mr. Olmert said he ordered the army to push forward with efforts “to strike terrorists and those who sent them and those who sponsor them. … None of them will be immune.”